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polyTop: Software for Computing Topology of Smooth Real Surfaces

  • Danielle A. Brake
  • Jonathan D. Hauenstein
  • Margaret H. ReganEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)

Abstract

A common computational problem is to compute topological information about a real surface defined by a system of polynomial equations. Our software, called polyTop, leverages numerical algebraic geometry computations from Bertini and Bertini_real with topological computations in javaPlex to compute the Euler characteristic, genus, Betti numbers, and generators of the fundamental group of a smooth real surface. Several examples are used to demonstrate this new software.

Keywords

Numerical algebraic geometry Topology Cell decomposition Graphs Euler characteristic Betti numbers Fundamental group 

Notes

Acknowledgments

The authors thank Mikael Vejdemo-Johansson for input regarding javaPlex. All authors acknowledge support from NSF ACI-1440607/1460032. Additional support for JDH was provided by Sloan Research Fellowship BR2014-110 TR14 and for MHR by Schmitt Leadership Fellowship in Science and Engineering.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Danielle A. Brake
    • 1
  • Jonathan D. Hauenstein
    • 2
  • Margaret H. Regan
    • 2
    Email author
  1. 1.Department of MathematicsUniversity of Wisconsin-Eau ClaireEau ClaireUSA
  2. 2.Department of Applied and Computational Mathematics and StatisticsUniversity of Notre DameNotre DameUSA

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